Permafrost currently stores more than a fourth of global soil carbon. A warming climate makes this carbon increasingly vulnerable to decomposition and release into the atmosphere in the form of greenhouse gases. The resulting climate feedback can be estimated using land surface models, but the high complexity and computational cost of these models make it challenging to use them for estimating uncertainty, exploring novel scenarios, and coupling with other models. We have added a representation of permafrost to the simple, open-source global carbon–climate model Hector, calibrated to be consistent with both historical data and 21st century Earth system model projections of permafrost thaw. We include permafrost as a separate land carbon pool that becomes available for decomposition into both methane (CH4) and carbon dioxide (CO2) once thawed; the thaw rate is controlled by region-specific air temperature increases from a preindustrial baseline. We found that by 2100 thawed permafrost carbon emissions increased Hector’s atmospheric CO2 concentration by 5 %–7 % and the atmospheric CH4 concentration by 7 %–12 %, depending on the future scenario, resulting in 0.2–0.25 ∘C of additional warming over the 21st century. The fraction of thawed permafrost carbon available for decomposition was the most significant parameter controlling the end-of-century temperature change in the model, explaining around 70 % of the temperature variance, and was distantly followed by the initial stock of permafrost carbon, which contributed to about 10 % of the temperature variance. The addition of permafrost in Hector provides a basis for the exploration of a suite of science questions, as Hector can be cheaply run over a wide range of parameter values to explore uncertainty and can be easily coupled with integrated assessment and other human system models to explore the economic consequences of warming from this feedback.